Joint dynamics calculation involves a large number of trigonometric operations, but the classic CORDIC (Coordinate Rotation Digital Computer) algorithm struggles to balance accuracy, speed, and resource consumption. This paper proposes an improved ITMI_CORDIC (Improvement through Merged Iterations CORDIC) algorithm for FPGA (Field Programmable Gate Array)-based real-time calculation of joint dynamics. Simulation verification shows that compared with the classic CORDIC algorithm, the model built with the ITMI_CORDIC algorithm reduces output delay by 46.7% and hardware overhead by 40.2%, with an error of less than 0.3%, thus meeting the requirements for real-time performance, accuracy, and hardware overhead simultaneously.